ANALYTICAL CHEMISTRY, VOL. 51, NO. 1, JANUARY 1979
91
Enzyme Electrode for Inhibitors Determination: Urease-Fluoride System Canh Tran-Minh" and Jacques Beaux €cole Nationale Supdrieure des Mines de Saint-Etienne, 158, cows Fauriel, 42023 Saint-Etienne Cddex, France
An enzyme electrode is constructed and optimized for inhibitor determination. The urease electrode inhibited by fluoride ions is chosen as an example to illustrate the procedure. The enzyme is chemically bound with glutaraldehyde to a silicone membrane which is part of the COz gas electrode. The inhibition reversibility is tested and various parameters related to the enzyme cross-linking technique are studied separately. The theoretical and experimental behaviors of the enzyme electrode as a function of inhibitor concentration are compared by analyzing the steady-state substrate and product concentration profiles inside the active layer. This study defines the optimum operating conditions for the use of an enzyme electrode.
I n recent years, the development of immobilized enzymes has contributed t o a rapid expansion of their use in t h e analytical field ( I , 2 ) . A large number of these studies dealt with the construction of enzyme electrodes for t h e determination of organic and biological compounds (glucose, urea, amino acids, . . .) ( 3 , 4 ) . Although these electrodes offer many advantages: reusability, greater stability and selectivity, they are limited t o the determination of substrates by measuring the consumption of a co-substrate (3)or the generation of the reaction product. T h e present paper is concerned with the construction and study of an enzyme electrode for the determination of a species which inhibits the enzyme bound to the specific electrode. For this purpose, an urease electrode was used as this enzyme gives rise t o a reversible inhibition by fluoride ions ( 5 ) . T h e behavior of the enzyme electrode has been studied as a function of parameters related to the enzyme immobilization technique in order t o obtain a n optimized response of t h e electrode t o t h e inhibitor. Understanding of the inhibition phenomenon is facilitated by a theoretical analysis of the steady-state substrate and product concentrations in the active layer for various inhibitor concentrations.
EXPERIMENTAL Reagents. Crease was provided by Sigma (powder from Jack Bean, type VI) 5.1 Sigma units/mg. One Sigma unit of urease activity is the amount of enzyme that will liberate 1 mg of ammonia nitrogen from urea in 5 min at pH 7 a t 30 "C. (One Sigma unit will also liberate 11.4 pmol of NH3 per min from urea a t pH 7.0 at 25 "C.) Human serum albumin (HSA) was provided by the Centre de Transfusion Sanguine de Lyon. The solution contained 20 g per 100 mL. Glutaraldehyde was a 25% solution in water, obtained from PROLABO. Other reagents were analytical reagents or laboratory grade materials. De-ionized water was used in all procedures. Apparatus. A PCO,electrode, from Radiometer (ref E 50361, was used as a basic electrode on which urease was bound for the determination of fluoride ions. This electrode was connected either to a pH meter "Radiometer pHM64" or to a "Tacussel" recorder with a TVED electrometric unit. Electrode Preparation. Various amounts of urease were dissolved in human serum albumin (HSA) solution. Ten pL of 0003-2700/79/035 1-0091$01 OO/O
this solution were deposited on the flat surface of the silicone membrane of the Pcol electrode, then various amounts of glutaraldehyde solution were mixed with HSA solution. The mixture was spread all over the surface of the silicone membrane. Cross-linking was performed at room temperature (22 "C) until complete solidification. Various binding times were used to improve the response of the electrode to the inhibitor. The electrode was then washed by immersion in a phosphate buffer solution (pH 7.0, 0.25 M), and rinsed with a glycine solution and then with water to neutralize the exccbss of glutaraldehyde. The thickness of the enzyme layer is about 60-120 pm. Assay Procedure. A phosphate buffer solution (pH 7.0,0.25 M) was placed in a thermostatically controlled cell a t 25 "C and stirred at a moderate speed with a magnetic stirrer. The electrode was immersed in this solution and when the electrode potential reached a stable value, urea was added up to a concentration of 10 M urea. The electrode potential was then recorded and used as a reference. From this reference state, various amounts of fluoride (NaF) were added to inhibit the enzyme. A stable value of the electrode potential was then obtained for each concentration of the inhibitor and a calibration curve of the electrode response was plotted as a function of inhibitor concentrations.
RESULTS I n order for a n enzyme electrode to be analytically useful, its steady-state response should be obtained rapidly after the measurement is initiated and must be quantitatively related t o the enzyme inhibitor. This assumes (a, t h a t the inhibitor rate is a t least as high as the enzymic velocity, and (b) t h a t t h e inhibition reaction is reversible. Reversibility of Inhibition by Fluoride Ions. T h e reversibility of urease inhibition can be demonstrated by measuring t h e activity of the immobilized enzyme before inhibition, in the presence of t h e inhibitor, and once again without any inhibitor. For this purpose, the experiments were carried out by dipping t h e urease electrode first in a urea phosphate buffer (UPB) solution containing lo-' M urea. A stable value of the electrode response was recorded and used as a reference. T h e electrode was then dipped in the U P B solution containing various amounts of NaF. Figure 1 shows t h a t the response time of t h e electrode t o fluoride ions is about 5-6 min. When t h e concentration of fluoride increases, a stable value of the potential can be found for each concentration of t h e inhibitor. When the concentration of fluoride decreases, the same values of the potential can again be observed for t h e same concentration of t h e inhibitor. Inhibition is reversed simply by lowering t h e concentration of inhibitor in the U P B solution. Effect of Incubation Time on the Electrode Response. T h e steady-state response of t h e enzyme electrode is not affected by the incubation time. T o prove this, the enzyme electrode was left u p to 4 days in contact with the inhibitor a t the same concentration: 5 X 10 M N a F in phosphate buffer (pH 7.0,0.25 M). Urea was then added so that the urea concentration reached M. T h e electrode response as a function of incubation time, T , is shown in Figure 2 . T h e stable value of the potential for a given inhibitor concentration is unchanged whatever t h e incubation time. Determination of Fluoride Ions. A typical calibration curve of a n enzyme electrode which is sensitive to N a F is C 1978 American Chemical Society
92
ANALYTICAL CHEMISTRY, VOL. 51, NO. 1, JANUARY 1979
cmv:
- LC
[
[ -
-120
6 min
I
t ime
Figure 1. Urease electrode response to fluoride ions (2 X M, 5 X M, and 2 X lo-* M) in phosphate buffer solution containing lo-* M urea
I
I
1D’
I
10-
Figure 4. Percentage inhibition as a function of fluoride conceritration for various amounts of immobilized enzyme (expressed in Sigma units)
-a -80
T .1 &y
T-4 days -100 * 5 min
time
Figure 2. Effect of incubation time Ton the electrode response to M), Dashed line shows the electrode response fluoride ions (5 X to urea (lo-’ M) and then to F- (5 X M)
Figure 3. Typical calibration curve of enzyme electrode sensitive to fluoride ions
presented in Figure 3. A linear range can be found between 3 X and lo--*M NaF, where the potential is nearly proportional to the logarithm of the NaF concentration. Below 3x M NaF, the curve exhibits a plateau corresponding t o the detection limit of the enzyme electrode. P e r c e n t a g e Inhibition. The inhibition process can be characterized by a percentage inhibition defined by the following expression: percentage inhibition =
( ;E;: )
1- -
x 100
where [PI: and [PI: are the product concentration in the active layer close to the electrode surface with and without inhibitor for the same urea concentration. As the percentage inhibition is a dimensionless parameter, it is a property that would facilitate the investigation by numerical analysis. Effect of Amount of Enzyme Used for Cross-Linking. Enzyme active layers bound to the Pco2electrode had approximately the same area and the same thickness. Various
Figure 5. Electrode response to urea taraldehyde concentration
M) as a function of glu-
Figure 6. Percentage inhibition as a function of fluoride concentration for various glutarakiehyde concentration expressed in YO(w/w): (a) 8.75, (b) 6.25, (c) 3.75, (d) 2.5, (e) 1.25
amounts of urease ranging from 0.05 to 1 Sigma unit were dissolved in 10 PI, of the HSA solution and deposited on the electrode silicone membrane before cross-linking by 2 pL of the glutaraldehyde solution. An amount of enzyrnic protein ranging from approximately 10 pg to 0.2 mg is then immobilized on the electrode. T h e binding time was 10 min. T h e response of the urease electrode to urea 10 M gives the same stable value but the percentage inhibition is a linear function of NaF concentration for each amount of urease used for cross-linking (Figure 4). These straight lines are translated to the right to high fluoride concentrations when the amount of enzyme used increases. The detection limit of the electrode is lower when the enzyme concentration decreases. E f f e c t of C o n c e n t r a t i o n of C r o s s - L i n k i n g Agent. Glutaraldehyde was used as the cross-linking agent which performed the immobilization of the enzyme. When the glutaraldehyde concentration is high enough, a denaturation reaction proceeds, leading to a decrease of the enzyme activity. T h e Figure 5 shows the response of the urease electrode to M as a fnnction of glutaraldehyde concentration. urea Similarly, the percentage inhibition is translated to the left to low inhibitor concentrations when the concentration of
ANALYTICAL CHEMISTRY, VOL. 51, NO 1 , JANUARY 1979 I % '00
t
00
-
I
93
e/*
100
50
4
14'
lo-'
M
b FI
Figure 9. Percentage inhibition as a function of fluoride concentration to 5 X lo-* M for various substrate concentrations ranging from
Percentage inhibition as a function of fluoride concentration for various values of binding time T'
Figure 7.
rnv -20 -LO
, -10''
M
~ 3 x 1 6 'k'
I---+[ X..
X.0
Figure 10.
Schematic representation of "nzyme electrode sensitive
to inhibitor
[UREA]
Electrode response to urea for various inhibitor (NaF) concentrations C , Figure 8.
glutaraldehyde increases as shown in Figure 6. This means that the higher the concentration of glutaraldehyde, the lower the detection limit of the electrode to fluoride ions. Effect of Binding Time. The cross-linking reaction depends essentially upon the binding time during which glutaraldehyde was left in contact with the proteins: enzyme and albumin. If the binding time was too short, the coating was fragile and easily torn; if too long. the enzyme layer became less active. When 5 units of urease in 10 pL of HSA solution were deposited on the tip of the electrode, and 2 bL of glutaraldehyde were added, the mixture was allowed to react for various binding times, T'ranging from 5 to 45 min. The response of the electrode to urea lo-* M is roughly the same. but the longer the binding time, the lower the detection limit of the electrode to fluoride ions (Figure 7 ) . The percentage inhibition is translated to high fluoride concentrations when the binding time becomes qhorter. Effect of Substrate Concentration. When an urease membrane is prepared according to the above-mentioned procedure with 30 min of binding-time, the inhibition effect of fluoride ions upon the electrode response can be plotted as a function of substrate concentrations (Figure 8). From this figure. a percentage inhibition can be obtained (Figure 9) showing that the percentage inhibition increases with the substrate concentration. This agrees with the process of uncompetitive inhibition ( 5 ) of the enzyme by its inhibitor.
DISCUSSION The response curves of enzyme electrodes for inhibitor determination can be predicted by analyzing the steady-state concentration profiles of the substrates and the products inside
the active layer. The parameters affecting the response of the electrode to inhibitors are given 7y the following kinetic study. Basic Model. Figure 10 shows thr $ask model used in this paper, where [SI,and [PI, are the coilrentrations of substrate and product in the bulk solution. A. Lhe diffusion of various species proceeds essentially in the ;,c.tive layer, the concentration of the product is assumed tc he nearly equal to zero a t the outer surface of the probe. Considering that fluoride ions exhibit an uncompetitive inhibition upon urease ( 5 ) ,the rea( ions can be written: k+,
k+2
E+S+ES--F k ,
+P
(1)
k-3
where I is the inhibitor, E the free ( .lzyme, ES and ESI the complexes enzymesubstrate and enz\ inesubstrate-inhibitor. S and P are the substrate and reactit 11 product, respectively. This t-ype of reversible inhibition is ot completely overcome by high substrate concentration. In homogeneous solution, the en/ me-catalyzed reaction is usually followed by monitoring eith, r the rate of appearance of the product P or the disappearanct )f the substrate S. The Michaelis-Menten equation then e ::)resses the rate of the reaction in the absence of inhibito in the simplest single substrate reaction system
where K," is the Michaelis conqtant tnd V," the maximum velocity proportional to the enzymr -oncentration [E],:
V I " = h+2[F
(4)
The rate of the reaction in the pres *iceof an uncompetitive inhibitor is modified by a term (1 + 1 . KI) which affects both \7m0 and K,"
94
ANALYTICAL CHEMISTRY, VOL. 51, NO. 1, JANUARY 1979
'f
X
Km" [I] I L -
+
L I
KI
where [I] is the inhibitor concentration. Therefore, if we represent r = 1 + [I]/K,, V, = Vmo/r,K, = Km"/ r ; the previous expression simplifies t o give:
This equation is similar to the simple Michaelis-Menten equation for a single substrate reaction and predicts for enzymes in the presence of an uncompetitive inhibitor, similar saturation kinetics to normal enzyme reactions. This expression may be used for the determination of V , and K , from a double reciprocal plot but is only valid for homogeneous solutions containing substrate and dissolved enzyme. In the case of an immobilized enzyme, the Lineweaver-Burk plot cannot be applied because the reaction rate is also affected by the diffusion of both substrate and product. A theoretical approach has been made by the use of differential equations related to both diffusion and to the chemical reaction. Once solved, these equations give rise to concentration profiles of substrate and product in the active layer in contact with the electrode. A comparison is then possible between the calculated and the experimental concentrations a t the interface electrode-active layer, since an electrode can be chosen which is sensitive to either the substrate (usually a co-substrate) or to the reaction product. Concentration Profiles of Substrate and Product in the Active Layer. As soon as an enzyme electrode is dipped into a buffer solution containing a substrate and an inhibitor, both of these compounds diffuse into the active layer giving rise t o ES and ESI complexes according to the previous equilibria, Equations 1 and 2. Thus, before a steady-state is reached, there is a consumption of both substrate and inhibitor. The steady-state is obtained when the concentrations of ES and ESI remain unchanged over all the active layer. At that moment, the rate of appearance of the product P is the same as the rate of disappearance of the substrate S but there is no consumption of the inhibitor. As the volume of the electrode active layer is much smaller than that of the buffer solution containing substrate and inhibitor, the amount of inhibitor removed by the immobilized enzyme during the nonsteady-state can be neglected. The same assumption is usually made for the substrate when an enzyme electrode is used for a substrate determination (6). As there is no consumption of inhibitor inside the active layer, at the steady state, the inhibitor concentration is assumed to be the same in this region. Therefore the steady-state concentrations of substrate and product can be determined by solving the following equations of diffusion coupled with enzymic reaction (6-8).
d2[P]
DP a x 2 -t vm K ,
[SI
+ [SI = o
where D , and D , are effective diffusion coefficients of S and P in the active layer, and x the distance of each point of the active membrane to the external surface of the active layer. These equations can be solved by numerical analysis on computer. T h e use of the following dimensionless reduced
0.5
-
3
L..
,-
I
x=e
X=J
Figure 11. Calculated concentration profiles of substrate ( - - ) and product (-) in the active layer as a function of inhibitor concentration [ 1;. The concentrations of substrate and product are expressed in K,', Vm0 = mol L-ls-', K," = IO-* mol L-', e = 2.5 X cm, D , N D, = 1.2 X cm' s-'. Inhibitor concentration [I]is expressed [IIIK,) in terms of r = (1
+
1
0.1
10
1
r-
Lb J.
K
Figure 12. Calculated product concentration [P at the electrode surface as a function of substrate concentration [SI in the bulk solution for various inhibitor concentrations expressed in r = (1 [IIIK,)
+
variables allows the results to be extended to other enzyme-inhibitor systems:
We assume for simplicity that the diffusion coefficient of the substrate and product are equal ( D , = Dp),the V, and K, values are constant over all the active layer. Figure 11 shows the calculated concentration profiles of substrate and product in the active layer as a function of inhibitor concentrations [I] expressed in terms of r = (1 + [I]/Kl) for a concentration of substrate [SI, = K," in the bulk solution. Effect of Substrate Concentration. When using various substrate concentrations [SIo in the bulk solution, the calculated product concentration [PIe close to the electrode surface at steady state can be expressed as a function of [SIo for various inhibitor concentrations (Figure 12). This is the usual way of expressing the response curve of an enzyme electrode for a substrate determination. The calculated percentage inhibition is plotted as a function of inhibitor concentration for various substrate concentrations (Figure 13). The curves on Figures 1 2 and 13 should be compared with the experimental ones shown in Figures 8 and 9 where the substrate is urea and the inhibitor is fluoride ions.
ANALYTICAL CHEMISTRY, VOL. 51, NO. 1, JANUARY 1979
I
-1.
t
Figure 13. Calculated percentage inhibition as a function of inhibitor concentration [I] for various substrate concentrations expressed in Km"
I7. 100
t
1
I
_
fl K.
10
Figure 14. Calculated percentage inhibition as a function of inhibitor concentration [I] for various enzyme activities Vm0 expressed in mol L"s-': (a) 5 X (b) (c) 2 X (d) 3 X (e) 5 X (f) lo-', (9)2 X lo-', (h) 3 X IO-'
Similar results can be found between experimental and theoretical curves as the experimental Michaelis constant and inhibitor constant are K," N 1.2 X lo-' M and K I 3 X 10-5 M, respectively. Effect of the Maximum Rate V," of the Reaction. The maximum rate Vm0is related to the concentration of enzyme by the equation:
V,"
= h,, [Elo
(9)
where
[E]" = [E] + [ES] + [ESI]
(10)
[E]" is the concentration of active immobilized enzyme. Vm0 is then a function of the proportion of active enzymes after immobilization which depends both on binding-time (Figure 7) and cross-linking agent (Figures 5, 6). For a given binding-time and a given glutaraldehyde concentration, V,' is usually proportional to the initial amount of enzyme to be cross-linked. Figure 14 reports the percentage inhibition as a function of inhibitor concentration expressed in terms of r for various V,". A translation to the right is observed when V," increases, as found in previous experimental results (Figure 4) for the urease-fluoride system. T h e detection limit is displaced toward high inhibitor concentration when Vmo increases. This can be explained on
95
Figure 11 where concentration profiles of substrate and products are given as a function of r. For an inhibitor concentration with r < 20, all the substrate molecules are consumed before reaching the electrode surface, so that the product concentration at the electrode surface is the same but high enough for the percentage inhibition to be zero. In this region, the enzyme electrode cannot detect any inhibitor. For an inhibitor concentration with r > 20, the activity of the immobilized enzyme is low enough so that part of substrate can reach the electrode surface and affect the product concentration a t this interface. In this case, the enzyme electrode can act as a sensor of inhibitors since increasing concentration of inhibitor linearly decreases the product concentration [PI, (Figure 3). When using glutaraldehyde as a cross-linking agent, its concentration affects the activity of the enzyme and therefore V,". High glutaraldehyde concentrations decrease V," and lower the detection limit of the enzyme electrode. This electrode exhibits a similar behavior for long binding times where a lower detection limit of fluoride ions has been found. Long binding times denature the enzyme and then decrease V,". The horizontal shift of the curves as a function of either glutaraldehyde concentration or binding time is characteristic of the variation of enzyme activity, in agreement with the previous theoretical interpretation.
CONCLUSION Our aim was not to construct an electrode specially for fluoride ion determination. An electrode using LaF, crystal membrane doped with Eu2+has been described a long time ago (9) and its characteristics and performances are wellknown. In this paper, we try to show the possibility of using an enzyme electrode for inhibitor determination whatever the inhibitor may be. The system urease-fluoride ions is given only as an example to illustrate the procedure which can be extended to other enzyme-inhibitor couples ( I O ) . The behavior of these electrodes as a function of various parameters could be explained by a theoretical analysis of the concentration profiles of substrate and product in the active layer. This investigation shows the conditions necessary to make an enzyme electrode sensitive or not to a given inhibitor. For substrate determinations, where the influence of the inhibitors must be low, an enzyme electrode must include a great amount of immobilized enzyme and high enzyme activity (high Vmo). On the other hand, the enzyme electrode requires a low immobilized enzyme concentration to be effective for the inhibitor determination. LITERATURE CITED (1) G. G. Guilbauit, "Handbook of Enzymatic Methods of Analysis", M. Dekker, New York, 1976. (2) M. M. Fishman. Anal. Chem., 50, 261H (1978). (3) S.Updike and G. Hicks, Nature (London), 214, 986 (1967). (4) G. G. Guiibault, R . K. Smith, and J. G. Montalvo, Anal. Chem., 41, 600 (1969). (5) G. Cimasoni, Rev. Mens. Suisse Odonto-Stomatol., 79, 911 (1969). (6) C. Tran-Minh, Thesis, Rouen, France, A 0 6262,CNRS (1971). (7) P. W. Carr, Anal. Chem., 49, 799 (19y77). (8) C. Tran-Minh and G. Broun. Anal. Chem., 47, 1359 (1975). (9) M. S. Fraut and J. W. Ross, Science, 154, 3756 (1966). (10) A . Townshend Process Biochem., 8(3), 22 (1973).
RECEIVED for review July 25,1978. Accepted October 12,1978.
